Course Slides
These will be posted here after each class.
If there are proofs or explanations that were discussed but which don't appear in the slides, email Julia and she will try to post them up.
Notes for Lecture 1 (Now with homework solution!)
Notes for Lecture 2 (including homework problem and discussion)
Calculus applets - I particularly recommend the "Area of a circle" (for Archimedes' method of exhaustion), "Limit of a sequence" and "Riemann sums and area under a curve".
Visualising the derivative - see how you calculate the slope of a curve by taking approximations of (change in y)/(change in x).
Lecture 3: Bayesian Statistics
Here are the bad statistics articles we discussed: Double yolks story (Daily Mail), Stone Age sat-nav (Daily Mail) (also reported a year later (also in the Daily Mail) and in the Telegraph), perfect Whist deal (originally published in the Mirror, 1998)/a>.
What Educated Citizens Should Know About Statistics and Probability by Jessica Utts
Lecture 4: Symmetries and groups (4Mb file) or Lecture 4 as a PDF (1.4Mb)
Notes for Lecture 4 (including the homework problem and a description of the classification of finite simple groups)
Symmetries of a dodecahedron - in particular look at the coloured multiplication table halfway down the page, which shows how mixed up all the symmetries are.
Solution to homework problem (multiplication table of symmetries of the square)
Lecture 5: Graphs and networks
A web comic you might appreciate!
A travelling salesman problem for the Olympic torch - did they get the shortest route?
Lecture 6: Chaos and fractals (beware: 35Mb!!! Probably that giant Mandelbrot zoom...) or Lecture 6 as a PDF (2.7Mb)
Lemming modelling spreadsheet - try changing the value of r (in F2) and see what happens! (This is the average number of babies per lemming.) Can you find the value for r at which periodic behaviour changes to chaotic behaviour? How about finding any of those 'islands of stability' in the bifurcation diagram?
Pascal's Triangle handout - colour the odd numbers and see the amazing fractal pattern!
Lecture 6 notes and homework (Now with homework solution!)
Lecture 7: Non-Euclidean geometry
Handout for Lecture 8 with more games to try
Solutions to two of the problems in the handout (New!)
The game-theoretic way to play Golden Balls
Lecture 9: An infinity of infinities
Notes for Lecture 9 (including two homework problems and an alternative version of Cantor's diagonal argument)
Dangerous Knowledge - A BBC documentary examining the life and work of Cantor, Boltzmann, Gödel and Turing.
Horizon: To infinity and beyond - Documentary about the story of infinity, including a clip of the mathematician who doesn't believe in infinity (about 22 minutes in).
Notes for Lecture 10, including a proof of why the two formulas for the zeta function are equivalent.
